Question
Multiply polynomial $ \, \color{blue}{ x^2+14x+40 } \, $ by $ \, \color{orangered}{ -6x-1 }$.
Answer
$$ \left( \color{blue}{x^2+14x+40} \right) \cdot \left( \color{orangered}{-6x-1} \right) = -6x^3-85x^2-254x-40 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{14x} & \color{blue}{40} \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{14x} & \color{blue}{40} \\ \hline \color{blue}{-6x} & \color{orangered}{-6x^3} & \color{orangered}{-84x^2} & \color{orangered}{-240x} \\ \hline \color{blue}{-1} & \color{orangered}{-x^2} & \color{orangered}{-14x} & \color{orangered}{-40} \\ \hline \end{darray} $$Combine like terms:
$$ -6x^3-84x^2-x^2-240x-14x-40 = \\ -6x^3-85x^2-254x-40 $$This page was created using
Polynomial Operations Calculator